Identifiability at the boundary for first-order terms

Abstract

Let Ω be a domain in R ⁿ whose boundary is C ¹ if n≥3 or C ^1,β if n=2. We consider a magnetic Schrödinger operator L _{W , q} in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for L _{W , q} . We also consider a steady state heat equation with convection term Δ+2W·∇ and recover the boundary values of the convection term W from the Dirichlet to Neumann map. Our method is constructive and gives a stability result at the boundary.

Keywords:

• Inverse problem
• Magnetic Schrödinger operator
• Boundary determination
• AMS Subject Classification: 35R30

Acknowledgements

R. M. B. was supported, in part, by the US National Science Foundation and M. S. was supported partly by the Academy of Finland and by the Finnish Academy of Science and Letters, Vilho, Yrjö and Kalle Väisälä Foundation. The authors greatly acknowledge the hospitality which they received during their visits to the University of Washington.